Having dealt with this issue as well as self-inflicted corneal lacerations, a vet visit as fast as possible is best. Corneal ulcers, infections are even worse to deal with (trust me, been there, been treating that recently). They can check how deep this is, prescribe appropriate meds - you don't want to wait 48 hours - ample time for an infection to set in

Had that happen once to my Bogart in the middle of the night and got him to the vet first thing in the morning. In his case, the vet had to put him under and remove a flap of skin at the point of the scratch. He was on meds for weeks afterwards.